Calculating Force on Wheaties from Cheerios: 28 N

[goaliejoe35]

Homework Statement
A box of Cheerios (mass mC = 1.2 kg) and a box of Wheaties (mass mw = 3.7 kg) are accelerated across a horizontal surface by a horizontal force F applied to the Cheerios box. The magnitude of the frictional force on the Cheerios box is 1.6 N, and the magnitude of the frictional force on the Wheaties box is 6.3 N. If the magnitude of F is 28 N, what is the magnitude of the force on the Wheaties box from the Cheerios box?

The attempt at a solution

I need some help setting this up. Shouldn't the magnitudes of the forces applied by both boxes equal each other?

 

[goaliejoe35]

I was able to solve it.

 

[Moetasim]

I would approach this problem by first identifying the relevant equations and principles that can be used to solve it. In this case, we can use Newton's Second Law, which states that the net force on an object is equal to its mass multiplied by its acceleration (F=ma).

In this scenario, we have two boxes (Cheerios and Wheaties) that are being accelerated by a horizontal force (F). We also have information about the masses of the boxes (mC=1.2 kg, mw=3.7 kg) and the frictional forces acting on them (FC=1.6 N, Fw=6.3 N).

To solve for the force on the Wheaties box from the Cheerios box, we can use the equation F=ma and substitute in the values we have for the Cheerios box: 28 N = (1.2 kg)aC. Solving for the acceleration of the Cheerios box, we get aC=23.33 m/s^2.

Now, we can use this acceleration to solve for the force on the Wheaties box. Using the same equation, F=ma, we can substitute in the values for the Wheaties box: Fw=(3.7 kg)(23.33 m/s^2)=86.2 N. Therefore, the magnitude of the force on the Wheaties box from the Cheerios box is 86.2 N.

To address your concern about the magnitudes of the forces applied by both boxes, it is important to note that the force applied by the Cheerios box (F=28 N) is the net force on the system, which includes both boxes. Therefore, it is not necessary for the magnitudes of the forces applied by each box to be equal. In this scenario, the force applied by the Cheerios box is larger because it has a smaller mass and experiences less frictional force compared to the Wheaties box.